[R-sig-ME] comparing 2 models
Phillip Alday
phillip.alday at mpi.nl
Wed Apr 25 17:52:16 CEST 2018
In addition to the previous suggestions (CV/LOO and AIC comparison),
there is also Vuong's closeness test for non nested models. I haven't
used it myself, but a quick search suggests that a fair amount of
information about its use and misuse (in e.g. checking for
zero-inflation in Poisson models) is available.
One small note here: PzAlpha and HRV are both continuous predictors, so
they both contribute the same number of degrees of freedom to a model,
so you can compare (log) likelihoods directly instead of using AIC or
BIC because the number of parameters will be the same. (You still can't
do the LRT because amongst other things the chisq df will be 0.) This
also suggests the parameter counting concern is largely moot, as the
parameters and data are the same. (I'll let someone else more qualified
address the broader issue of parameter counting for AIC/BIC in mixed
models.)
There are also a number of parameter selection methods that work within
one model. In frequentist land, there's elastic net and LASSO, which are
implemented for mixed models in packages such as lmmen and glmmLasso.
There's two ways to use those methods here:
(1) cross validation on the penalty for number of parameters so that the
model selects the 'ideal' number of predictors
(2) setting a particularly penalty to achieve a desired number of
parameters and letting the model choose which ones those are
Both should be typically well supported in good elastic net and LASSO
implementations.
In Bayesian terms, you can achieve the same thing by appropriate choice
of priors. brms has LASSO and horseshoe priors and uses early the same
syntax as lme4:
sumModelInteraction4 <- brm(RT ~ 1 + (PzAlpha+ HRV+lnX+Drive)^3 + (1 |
Pnum) + (1 | Trial), data = INFAST_Behavioralnew,
prior=set_prior('horseshoe',class='b'))
(The author of brms, Paul Bürkner, also contributes to this list and
might be able to say more about ways of addressing this issue.)
Finally, I see that you're using untransformed RTs in a linear/gaussian
model. There's a lot of debate on whether you should transform or use a
non linear/gaussian model (e.g. log transform, use the gamma transform
with identity or inverse link, etc.). I would check to see how well the
current model actually describes the data and see if non-gaussian models
or a suitable transformation improves fit before doing variable selection.
Best,
Phillip
On 04/25/2018 01:47 PM, Jonathan Judge wrote:
> I think the best option would be to refit these models in Stan (a front end like rstanarm or brms makes it easy with similar lme4 syntax) and use the LOO function to compare their out of sample predictive power.
>
> Otherwise, if you wish to stick with lme4, you need some way to properly count the number of effective parameters. AIC doesn’t do that because it doesn’t understand / account for the shrinkage of random effects. You might consider WAIC, which does a better job of this. There is an implementation for lme4 models in the blmeco package.
>
> Jonathan
>
> Sent from my iPhone
>
>> On Apr 25, 2018, at 2:45 AM, Emmanuel Curis <emmanuel.curis at parisdescartes.fr> wrote:
>>
>> Hello,
>>
>> I think if your interest is more in predictive power of your model
>> than in its ability to reproduce the dataset, your best choice would
>> be using cross-validation. And to summarize the closeness of your
>> predicted results to the real ones, you may use all the concordance
>> tools, either descriptive like Bland-Altman plots, or more
>> quantititive like concordance correlation coefficients (but beware
>> that their interpretation beyond « the closest to one, the better » is
>> not easy) or similar agreement measures. Obviously, the second part
>> can be done without the cross-validation step, on your single, whole
>> dataset.
>>
>> The « best » model will be the one witht the highest concordance
>> correlation coefficient; to test that it is significantly better is
>> more tricky, but should be done with carefully crafted simulations,
>> fitting one model to simulated data generated by either one model or
>> the other and vice-versa...
>>
>> Note also that if all your predictors are continuous, as seems to be
>> in your description, the syntax (x+y+...)^n is misleading, because it
>> forgets some important terms.
>>
>> Indeed, let consider the two-variables case, x and y. The first order
>> model is z = µ0 + alpha * x + beta * y, a plane. The second order
>> model would then be a paraboloid,
>>
>> z = µ0 + alpha * x + beta * y + gamma * x² + delta * y² + a * x * y
>>
>> However, the syntax (x+y)^2 expends to x + y + x:y, that is it forgets
>> the I(x^2) and I(y^2) terms. So, unless you have strong belief that
>> both gamma and delta are 0, you're model is incomplete.
>>
>> Hope all of this will help,
>> Best regards,
>> Emmanuel
>>
>> On Tue, Apr 24, 2018 at 09:17:32PM -0400, P Greenwood wrote:
>> « Hello
>> «
>> « Although alpha-band EEG is something of a gold standard in predicting processing of stimuli (pre-stimulus alpha), it is not easy to measure EEG outside the lab (e.g. in a vehicle). In contrast, heart-rate and eye gaze are more reliably obtained in the field using low-cost wearable sensors.
>> «
>> « We sought to compare the ability of 3 sensors to model human reaction time (RT) to a signal from automation. We compared these measures: alpha-band (PzAlpha), heart-rate variability (HRV), and eye gaze (lnX). Each person has 10 trials in each of 5 drives. Pnum is subject number.
>> «
>> « We sought to model RT from alpha-band, heart-rate variability (HRV), and eye gaze (lnX) and Drive.
>> «
>> « sumModelInteraction4 <- lmer(RT ~ 1 + (PzAlpha+ HRV+lnX+Drive)^3 + (1 | Pnum) + (1 | Trial), data = INFAST_Behavioralnew, REML = FALSE)
>> «
>> « The output, pasted below, reveals interactions: PzAlpha x HRV, PzAlpha x Drive, and HRV x Drive. Also pasted below is some of the raw data.
>> «
>> « An LRT comparing this model with an additive model (PzAlpha+RMSSD+lnX+Drive+Trial) yields a significant difference. This suggests that the interactions PzAlpha x Drive and HRV x Drive are meaningful predictors.
>> «
>> « We would like to determine whether PzAlpha x Drive or HRV x Drive is the better predictor of RT. What is the best way to compare those 2 models? The measures are scaled and centered.
>> «
>> « Thank you very much.
>> «
>> « Pam Greenwood
>> «
>> « Fixed effects:
>> « Estimate Std. Error df t value Pr(>|t|)
>> « (Intercept) -1.908e-01 1.368e-01 3.310e+01 -1.395 0.17235
>> « PzAlpha -1.098e-01 6.042e-02 2.339e+02 -1.818 0.07041 .
>> « HRV -1.127e-01 6.402e-02 1.112e+03 -1.760 0.07868 .
>> « lnX 7.921e-02 7.547e-02 1.102e+03 1.050 0.29416
>> « Drive 5.382e-02 1.661e-02 1.080e+03 3.241 0.00123 **
>> « PzAlpha: HRV -1.586e-01 6.424e-02 7.035e+02 -2.468 0.01382 *
>> « PzAlpha:lnX 1.116e-01 7.400e-02 8.456e+02 1.508 0.13199
>> « PzAlpha:Drive 4.405e-02 1.730e-02 1.049e+03 2.546 0.01103 *
>> « HRV:lnX -4.723e-02 6.905e-02 1.100e+03 -0.684 0.49407
>> « HRV:Drive 3.652e-02 1.747e-02 1.098e+03 2.091 0.03677 *
>> « lnX:Drive -1.275e-02 1.992e-02 1.100e+03 -0.640 0.52217
>> « PzAlpha: HRV:lnX 1.473e-02 2.567e-02 8.244e+02 0.574 0.56621
>> « PzAlpha: HRV:Drive 3.308e-02 1.878e-02 1.084e+03 1.761 0.07845 .
>> « PzAlpha:lnX:Drive -2.325e-02 2.005e-02 9.166e+02 -1.160 0.24640
>> « HRV:lnX:Drive 9.729e-03 1.769e-02 1.097e+03 0.550 0.58247
>> «
>> «
>> «
>> « Pnum
>> « Drive Trial RT ACC FzAlpha CzAlpha PzAlpha FzTheta CzTheta PzTheta MeanPupil lnX lnY MeanRR
>> « HRV
>> « 20 1 1 1480.8931 1 7.9928 10.216 7.6254 3.4916 4.8657 6.4977 4.280969072 -3.208115816 -2.423813328 0.7336 0.074666667
>> « 20 1 2 1983.254 1 -8.2609 0.62018 0.32812 4.2257 6.0181 6.5564 4.360414101 -1.926558582 -2.364252526 0.7336 0.074666667
>> « 20 1 3 1588.0317 1 1.2572 5.5394 9.0619 4.322 6.7421 7.2778 4.429370379 -2.510514134 -2.890876402 0.734 0.073333333
>> « 20 1 4 2600 0 -2.0822 -3.5216 2.597 7.6632 9.4505 9.2404 3.994177574 -2.121340179 -3.875411777 0.7408 0.050666667
>> « 20 1 5 1268.9969 1 2.463 4.5837 4.0916 3.4363 4.2989 -2.1573 3.927884406 -1.754642861 -2.737213207 0.7516 0.014666667
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>> « Editorial Board, NeuroImage
>> « David King Hall 2052
>> « George Mason University
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>> «
>> « Ph: 703 993-4268
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>> « email: Pgreenw1 at gmu.edu
>> « http://psychology.gmu.edu/people/pgreenw1
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>> « _______________________________________________
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>>
>> --
>> Emmanuel CURIS
>> emmanuel.curis at parisdescartes.fr
>>
>> Page WWW: http://emmanuel.curis.online.fr/index.html
>>
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